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ArtMath - The Lure of the Abstract tracing the parallel...

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The Lure of the Abstract: tracing the parallel influences of the zeitgeist on Art and Mathematics in the last 200 years Feb. 21, 2006, Univ. of Washington
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OUTLINE Why do math and art have anything to do with each other? Jackson Pollock and the Atomic Bomb Early 19 th century: Breaking the ties with the concrete and tangible Late 19 th century: Enlarging the aesthetic and playing with counter-factual universes 20 th century: Full blown abstraction
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The saga of mathematics is unknown outside a narrow coterie; the high points of art are basic ingredients of a liberal education. Can we use our knowledge of the latter to open up the former? There are stunning parallels between the development of the two. WHY?? Both fell in love with the abstract. There are few examples of direct contact/influence. Somehow, the zeitgeist seeps over the levees. Neither art nor math respects national boundaries; they are international languages. I want to use these links to explain to the math- phobic something of what has been going on in math.
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A first example of the uncanny Art/Math linkage, from post WWII America Beauty and power through randomness
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The discovery that randomness can be harnessed to create science and beauty, c.1945 Jackson Pollock, Autumn Rhythm, #30 , 1950
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Pollock’s “Action Painting” When the German emigré artist and intellectual, Hans Hoffmann, suggested to Jackson Pollock that he “observe nature” or his painting would become repetitious, Pollock – born in Cody, Wyoming –famously responded “f*** you, I am nature.” “Strict control is what Pollock gave up when he began to dribble and spatter … The actual shapes were largely determined by the dynamics of the material and his process: the viscosity of the paint, the speed and direction of its impact on the canvas … The result is so alive, so sensuously rich, that all earlier American painting looks pale by comparison.” (Janson, p.846)
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Nick Metropolis, Stan Ulam, and Johnny von Neumann at Los Alamos Von Neumann to Gen. Richtmeyer, 1947: I have been thinking a good deal about the possibility of using statistical methods to solve (nuclear devices) in accordance with the principle suggested by Stan Ulam. The more I think about it, the more I become convinced the idea has great merit.
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What is the Monte Carlo Method? An actual bomb has some 10000000000000000000000000 neutrons flying around inside it. Traditionally, one would try to model d(x,y,z,u,v,w,t), how many neutrons were at each point with each velocity at each time. Von Neumann said – let’s follow a small pollster’s sample of them – say 100! – using the ENIAC. Instead of keeping track of all the uranium nuclei, let’s just find the odds of each neutron hitting a nucleus at any given point, the odds of it splitting the nucleus, the odds of how many neutrons will come out and at what speeds and directions.
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